Question

In 2011, when the Gallup organization polled investors, 34% rated gold the best long-term investment. However, in April of 2013 Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 241 of the 1005 respondents chose gold as the best long-term investment.

• Do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorable rate, or do you think this is a sample variability? Explain your answer using the calculated statistics.

Answer 1

We have to test whether the  value of gold as a long-term investment have really changed from the old 34% favorable rate or not.

So, it is a two tailed hypothesis testing

Given that

po = 0.34 (population proportion)

p = x/n = 241/1005 (sample proportion)

sample size n = 1005

test statistic =

using z table to find - 6.7 in the left most column and 0.01 in the top row, then select the intersecting cell, we get

p value = 0.000

p value is less than 0.05 significance level, so we can reject the null hypothesis

Therefore, we can conclude that the proportion has really changed from 34%